Answer
Verified
405k+ views
Hint: To solve this question first we will find the SI unit of the given quantities in the option. We can do this simply by writing the mathematical expression or by breaking them into fundamental quantities. Then compare them with the SI unit given in the question to find the required answer.
Complete step by step answer:
SI unit or International System of Unit is based on meter, kilogram, second, ampere, kelvin candela and mole. It uses a set of prefixes to indicate the multiplication and division in terms of power of 10.
Resistance can be defined from Ohm’s law as,
$R=\dfrac{V}{I}$
Voltage can be defined as the product of electric field and distance. Electric field is defined in terms of force per unit charge. Dimension of charge is given by product of current and time.
So,
$R=\dfrac{V}{I}=\dfrac{\dfrac{Fd}{q}}{I}=\dfrac{Fd}{qI}=\dfrac{Fd}{It\times I}=\dfrac{Fd}{{{I}^{2}}t}$
Now, SI unit of force is, $kgm{{s}^{-2}}$
Si unit of current is A, SI unit of time is second and SI unit of distance is meter.
So, from the above equation we can write that the SI unit of resistance is,
$\dfrac{kgm{{s}^{-2}}m}{{{A}^{2}}s}=kg{{m}^{2}}{{A}^{-2}}{{s}^{-3}}$
Now, inductance is given by the mathematical expression as,
From above, the SI unit of voltage can be given as, $kg{{m}^{2}}{{A}^{-1}}{{s}^{-3}}$
SI unit of current is A and time is second.
Si unit of inductance will be, $\dfrac{kg{{m}^{2}}{{A}^{-1}}{{s}^{-3}}}{\dfrac{A}{s}}=kg{{m}^{2}}{{A}^{-2}}{{s}^{-2}}$
Capacitance can be defined as,
$C=\dfrac{Q}{V}=\dfrac{It}{V}$
So, the SI unit of capacitance will be, $\dfrac{As}{kg{{m}^{2}}{{A}^{-1}}{{s}^{-3}}}=k{{g}^{-1}}{{m}^{-2}}{{A}^{2}}{{s}^{4}}$
Magnetic flux can be given by the product of magnetic field and area.
$\phi =BA$
Magnetic field is given by Lorentz force as,
$B=\dfrac{F}{qv}=\dfrac{F}{Itv}$
The SI unit of magnetic field will be,
$\dfrac{kgm{{s}^{-2}}}{Asm{{s}^{-1}}}=kg{{A}^{-1}}{{s}^{-2}}$
So, SI unit of magnetic flux will be $kg{{A}^{-1}}{{s}^{-2}}\times {{m}^{2}}=kg{{m}^{2}}{{A}^{-1}}{{s}^{-2}}$
From the above calculation we find that SI unit of resistance is $kg{{m}^{2}}{{A}^{-2}}{{s}^{-3}}$
The correct option is (A)
Note: Sometimes we can express the derived physical quantities with more than one formula where we have different physical quantities. We can use any one of them. For example, if we consider the inductance, we can express it as magnetic flux per unit current flowing. If we take this expression also, we will get the same answer.
Complete step by step answer:
SI unit or International System of Unit is based on meter, kilogram, second, ampere, kelvin candela and mole. It uses a set of prefixes to indicate the multiplication and division in terms of power of 10.
Resistance can be defined from Ohm’s law as,
$R=\dfrac{V}{I}$
Voltage can be defined as the product of electric field and distance. Electric field is defined in terms of force per unit charge. Dimension of charge is given by product of current and time.
So,
$R=\dfrac{V}{I}=\dfrac{\dfrac{Fd}{q}}{I}=\dfrac{Fd}{qI}=\dfrac{Fd}{It\times I}=\dfrac{Fd}{{{I}^{2}}t}$
Now, SI unit of force is, $kgm{{s}^{-2}}$
Si unit of current is A, SI unit of time is second and SI unit of distance is meter.
So, from the above equation we can write that the SI unit of resistance is,
$\dfrac{kgm{{s}^{-2}}m}{{{A}^{2}}s}=kg{{m}^{2}}{{A}^{-2}}{{s}^{-3}}$
Now, inductance is given by the mathematical expression as,
From above, the SI unit of voltage can be given as, $kg{{m}^{2}}{{A}^{-1}}{{s}^{-3}}$
SI unit of current is A and time is second.
Si unit of inductance will be, $\dfrac{kg{{m}^{2}}{{A}^{-1}}{{s}^{-3}}}{\dfrac{A}{s}}=kg{{m}^{2}}{{A}^{-2}}{{s}^{-2}}$
Capacitance can be defined as,
$C=\dfrac{Q}{V}=\dfrac{It}{V}$
So, the SI unit of capacitance will be, $\dfrac{As}{kg{{m}^{2}}{{A}^{-1}}{{s}^{-3}}}=k{{g}^{-1}}{{m}^{-2}}{{A}^{2}}{{s}^{4}}$
Magnetic flux can be given by the product of magnetic field and area.
$\phi =BA$
Magnetic field is given by Lorentz force as,
$B=\dfrac{F}{qv}=\dfrac{F}{Itv}$
The SI unit of magnetic field will be,
$\dfrac{kgm{{s}^{-2}}}{Asm{{s}^{-1}}}=kg{{A}^{-1}}{{s}^{-2}}$
So, SI unit of magnetic flux will be $kg{{A}^{-1}}{{s}^{-2}}\times {{m}^{2}}=kg{{m}^{2}}{{A}^{-1}}{{s}^{-2}}$
From the above calculation we find that SI unit of resistance is $kg{{m}^{2}}{{A}^{-2}}{{s}^{-3}}$
The correct option is (A)
Note: Sometimes we can express the derived physical quantities with more than one formula where we have different physical quantities. We can use any one of them. For example, if we consider the inductance, we can express it as magnetic flux per unit current flowing. If we take this expression also, we will get the same answer.
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Summary of the poem Where the Mind is Without Fear class 8 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Write an application to the principal requesting five class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE